edu:topics:complex:start
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edu:topics:complex:start [2017/11/10 15:16] simon |
edu:topics:complex:start [2018/02/21 23:51] (current) simon [notes] |
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| √ −1, instead of being | √ −1, instead of being | ||
| called positive, negative and imaginary (or worse still, impossible) unity, been given the names say,of direct, inverse and lateral unity, there would hardly have been any scope for such obscurity. | called positive, negative and imaginary (or worse still, impossible) unity, been given the names say,of direct, inverse and lateral unity, there would hardly have been any scope for such obscurity. | ||
| + | </quote></quote> | ||
| + | |||
| + | ---- | ||
| + | just like calculus was re-defined in terms of limits to eliminate "impossible" infinities, so | ||
| + | complex numbers are redefined considering groups and sets ... but this requires a great deal more theory: | ||
| + | <quote></quote>http://www.math.uri.edu/~merino/spring06/mth562/ShortHistoryComplexNumbers2006.pdf<quote> | ||
| + | Augustin-Louis Cauchy (1789-1857) initiated complex function theory in an 1814 memoir | ||
| + | submitted to the French Acad´emie des Sciences. The term analytic function was not | ||
| + | mentioned in his memoir, but the concept is there. The memoir was published in 1825. | ||
| + | Contour integrals appear in the memoir, but this is not a first, apparently Poisson had | ||
| + | a 1820 paper with a path not on the real line. Cauchy constructed the set of complex | ||
| + | numbers in 1847 as R[x]/(x2 + 1) | ||
| + | <quote>We completely repudiate the symbol √ | ||
| + | −1, abandoning it without regret because | ||
| + | we do not know what this alleged symbolism signifies nor what meaning | ||
| + | to give to it. | ||
| </quote></quote> | </quote></quote> | ||
| Line 201: | Line 217: | ||
| ====notes==== | ====notes==== | ||
| - | [[edu:resources:schrodinger-life]] | [[edu:resources:gleick-chaos]] | galileo | | + | [[books:schrodinger]] | [[edu:resources:gleick-chaos]] | galileo | |
| copernicus | [[edu:resources:penrose-physics]] | copernicus | [[edu:resources:penrose-physics]] | ||
edu/topics/complex/start.1510287379.txt.gz · Last modified: 2017/11/10 15:16 by simon
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